Answer:
a) 820
b)450
c) -540
d) -294
e) 1440
f) 1425
Step-by-step explanation:
a) it is an arithmetic progression with ratio=4
a1=3,
a2=3+r=3+4=7.....
a20=a1+19r
so a20=3+19*4=3+76=79
S=(a1+an)*n/2 where n=20
so S=(3+79)*20/2=820
b) a15=a1+14*r=2+14*4=2+56=58
S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450
It is the same formula for all the exercises
S=(a1+an)*n/2 , where n is the number of terms
c) a40=30+39*(-3)=30-87=-57
So S=(30-57)*40/2=-540
d) a14=5+13*(-4)=5-52=-47
S=(5-47)*14/2=-42*14/2=-42*7=-294
e) it is 5+7+9+......+75
nr of terms = (an-a1) :r+1=(75-5):2+1=36
S=(5+75)*36/2=36*40=1440
f) ratio=7-4=3
the same formula for n= (91-4):3+1=87:3+1=29+1=30
S=(4+91)*30/2=95*30/2=2850/2=1425
I leaerned this neat trick
you don't need to convert to vertex form
where
y=ax^2+bx+c
the x value of the vertex is -b/2a
the y value is found by inserting the x value of the vertex into the equation
so
1x^2-6x+14
-b/2a=-(-6)/2(1)=6/2=3
plug that in
y=x^2-6x+14
y=3^2-6(3)+14
y=9-18+14
y=5
the vertex is (3,5)
Answer:
For 10 dozen cookies, you would need 32 cups of oats. Step by step:
Step-by-step explanation:
1 dozen = 12 cookies
10 dozen cookies = 120 cookies ( multiply 10 *12)
15 cookies *8= 120 cookies
If for every 4 cups of oats you have 15 cookies, then you need to multiply 4 by 8 to get it equal to the amount of 120 cookies. If you multiply 15 by 8, then you multiply 4 by 8, which gets you 32 cups of oats.
Hope this helps!
Answer:
9 and -5
Step-by-step explanation:
The only way to get a negative product is from one number to be negative and the other to be positive. And with that in mind, the only way to get positive 4 as a product is to have 9 be the positive number.
